Longitudinally measured phenotypes are important for exploring genetic and environmental factors that affect complex traits over time. Genetic analysis of multiple measures in longitudinal studies provides a valuable opportunity to understand genetic architecture and biological variations of complex diseases. In this paper, stochastic functional linear models are developed for temporal association analysis at gene levels to analyze sequence data and longitudinally measured quantitative traits. Functional data analysis techniques are utilized to reduce high dimensionality of sequence data and draw useful information. A variance-covariance structure is constructed to model the measurement variation and correlations of the traits based on the theory of stochastic processes. Spline models are used to estimate the time-dependent trajectory mean function. By intensive simulation studies, it is shown that the proposed stochastic models control type I errors well, and have higher power levels than those of the perturbation tests. In addition, the proposed methods are robust when the correlation function is mis-specified. We test and refine the models and related software using real data sets of Framingham Heart Study.

中文翻译：

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纵向研究中基于基因的数量性状关联分析的随机函数线性模型

纵向测量的表型对于探索随时间影响复杂性状的遗传和环境因素非常重要。纵向研究中多种测量的遗传分析为了解复杂疾病的遗传结构和生物学变异提供了宝贵的机会。在本文中，开发了随机函数线性模型，用于基因水平的时间关联分析，以分析序列数据和纵向测量的数量性状。功能数据分析技术用于降低序列数据的高维并提取有用信息。基于随机过程理论，构建方差-协方差结构，对性状的测量变异和相关性进行建模。样条模型用于估计时间相关的轨迹平均函数。通过深入的模拟研究，表明所提出的随机模型可以很好地控制 I 类错误，并且具有比扰动测试更高的功率水平。此外，当相关函数指定错误时，所提出的方法是稳健的。我们使用弗雷明汉心脏研究的真实数据集测试和改进模型和相关软件。